Explanation:

To determine the least positive value of A for which the number 34278A2597 is divisible by 9, we need to use the rule for divisibility by 9. A number is divisible by 9 if the sum of its digits is divisible by 9.

- Start by summing the given digits: 3 + 4 + 2 + 7 + 8 + A + 2 + 5 + 9 + 7 = 47 + A.

- Find the smallest value of A such that 47 + A is divisible by 9.

Check each option:

- Option 1, 7: 47 + 7 = 54, which is divisible by 9. Correct Answer

- Option 2, 2: 47 + 2 = 49, which is not divisible by 9.

- Option 3, 1: 47 + 1 = 48, which is not divisible by 9.

- Option 4, 8: 47 + 8 = 55, which is not divisible by 9.

Therefore, the least positive value of A that makes the number divisible by 9 is 7.

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